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Equation solver, step by step
Type an equation such as 2x + 3 = 7 or x² − 5x + 6 = 0, or a system of two or three equations, and see how to solve it, one step at a time. Answers are exact: fractions, square roots and complex numbers.
Solution
Your equation
Steps
Subtract 3 from both sides.
Divide both sides by 2.
Check: put x = 2 back into the equation. Both sides come to 7, so the answer is right.
What it can’t solve yet
- Equations with x³ or higher powers.
- An unknown in a denominator (1/x) or under a square root (√x).
- Absolute values, inequalities (<, >), and exponential, log or trig equations.
- Systems that aren’t linear, or with more than 3 equations.
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How to solve an equation step by step
- Type an equation, such as 3(x − 2) = x/2 + 1, or use the keys for x, ², √ and fractions. For a system, put each equation on its own line.
- Press Enter or Solve. For systems, choose elimination or substitution.
- Follow the steps: each line of working comes with a short explanation. Copy them to paste into your notes.
Questions
What kinds of equations can it solve?
Linear equations in one unknown, such as 2x + 3 = 7 or 3(x − 2) = x/2 + 1; quadratic equations, such as x² − 5x + 6 = 0; and systems of 2 or 3 linear equations in x, y and z. Brackets, fractions and decimals are fine, and any letter can be the unknown.
How do I type a system of equations?
Put each equation on its own line: press Shift+Enter or the new line key between them, or separate them with a semicolon, as in x + y = 3; x − y = 1. Use as many equations as unknowns. Then choose elimination or substitution for the steps.
When does it factor, and when does it use the quadratic formula?
When the roots are whole numbers or fractions, it factors: it finds two numbers that multiply to c (or a × c) and add up to b. With no x term it takes square roots, and with no number term it factors out x. Otherwise it uses the quadratic formula, x = (−b ± √(b² − 4ac)) / 2a.
Why do some answers look like 1 ± √2 or −1 ± 2i?
The solver keeps answers exact. When the discriminant isn’t a perfect square, the roots are square roots, simplified as far as they go, with decimals next to them. When it’s negative, there’s no real solution, and the two complex solutions use i, the square root of −1.
What do “no solution” and “infinitely many solutions” mean?
An equation like 2x = 2x + 1 is never true, so it has no solution. One like 2(x + 1) = 2x + 2 is always true, so every number works. A system has no solution when its equations contradict each other (parallel lines), and infinitely many when one equation repeats another.
What can’t it solve yet?
Equations with x³ or higher powers, an unknown in a denominator or under a square root, absolute values, inequalities, exponential and trig equations, and systems that aren’t linear or have more than 3 equations. It says so plainly when you type one.